Multiple high energy solutions for fractional Schrodinger equation with critical growth

作者：Guo, Lun; Li, Qi^*

来源：Calculus of Variations and Partial Differential Equations, 2022, 61(1): 15.

DOI：10.1007/s00526-021-02122-2

• POSITIVE SOLUTIONS
• LAPLACIAN
• EXISTENCE
• STATE

In this work, we study the following fractional Schrodinger equation with critical growth @@@ (-Delta)(s) u + V(x)u = vertical bar u vertical bar(2s)*(-2u), x is an element of R-N, @@@ where s is an element of (0, 1), N > 4s, (-Delta)(s) is the fractional Laplacian operator of order s, potential function V (x) : R-N -> R, 2(s)* = 2N/N-2S is the fractional critical Sobolev exponent. In virtue of a barycenter function, quantitative deformation lemma and Brouwer degree theory, we prove the existence and multiplicity of positive high energy solutions. Our results extend and improve the recent work on the existence of high energy solutions for fractional Schrodinger equation by Correia and Figueiredo (Cale Var Part Differ Equ 58:63, 2019).

• 单位
  复旦大学